It is somewhat surprising to learn the probability that 2 persons in a class share the same birthday As an approximation, assume that the 365 days are equally likely birthdays (a) What is the probability that, among 3 persons, at least 2 have the same birthday The reasoning associated with a tree diagram shows that there are 365 365 365 possible birthday outcomes Of these, 365 364 363 correspond to no common birthday ) (b) Generalize the above reasoning to N persons Show that We see that with N 23 persons, the probability is greater than 1 2 that at least two share common birthday ) P No common birthday 365 x 364 x x (365 N 1) (365) Some numerical values are 5 9 18 22 23 P No common 973 905 653 524 493 birthday

Question: It is somewhat surprising to learn the probability that 2 persons in a class share the same birthday. As an approximation, assume that the 365

It is somewhat surprising to learn the probability that 2 persons in a class share the same birthday. As an approximation, assume that the 365 days are equally likely birthdays.
(a) What is the probability that, among 3 persons, at least 2 have the same birthday? [The reasoning associated with a tree diagram shows that there are 365 Ã— 365 Ã— 365 possible birthday outcomes. Of these, 365 Ã— 364 Ã— 363 correspond to no common birthday.)
(b) Generalize the above reasoning to N persons. Show that

We see that with N = 23 persons, the probability is greater than 1/2 that at least two share common birthday.)

P[ No common birthday ] 365 x 364 x . . . x (365-N + 1) (365) Some numerical values are 5 9 18 22 23 P[ No common 973 905 .653 .524 .493 birthday ]

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